1. Lisp and Scheme I

2. Versions of LISP LISP is an acronym for LISt Processing language Lisp is an old language with many variants – Fortran is the only older language still in wide(?) use – Lisp is alive and well today Most modern versions are based on Common Lisp Scheme is one of the major variants Scheme – We’ll use Scheme, not Lisp, in this class The essentials haven’t changed much

3. Why Study Lisp? It’s a simple, elegant yet powerful language You will learn a lot about PLs from studying it We’ll look at how to implement a Scheme interpreter in Scheme Many features, once unique to Lisp, are now in “mainstream” PLs: python, javascript, perl, R … It will expand your notion of what a PL can be Lisp is considered hip and esoteric by some, but not all, computer scientists

4. LISP Features S-expression as the universal data type – either as atom (e.g., number, symbol) or a list of atoms or sublists Functional Programming Style – computation done by applying functions to arguments, functions are first class objects, minimal use of side-effects Uniform Representation of Data and Code – (A B C D) can be interpreted as data (i.e., a list of four elements) or code (calling function ‘A’ to the three parameters B, C, and D) Reliance on Recursion – iteration is provided too, but recursion is much more natural Garbage Collection – frees programmer from explicit memory management

5. What’s Functional Programming? FP: computation is applying functions to data Imperative or procedural programming: a program is a set of steps to be done in order FP eliminates or minimizes side effects and mutable objects that create/modify state FP treats functions as objects that can stored, passed as arguments, composed, etc.

6. Pure Lisp and Common Lisp Lisp has a small and elegant conceptual core that has not changed much in almost 50 years. McCarthy’s original Lisp paper http://www- formal.stanford.edu/jmc/recursive.pdf defined all of Lisp using just seven primitive functionshttp://www- formal.stanford.edu/jmc/recursive.pdf Common Lisp is large (> 800 built-in functions), has all the modern data-types, good programming environments, and good compilers.

7. Scheme Scheme is a dialect of Lisp that is favored by people who teach and study programming languages Why? – It’s simpler and more elegant than Lisp – It’s pioneered many new programming language ideas (e.g., continuations, call/cc) – It’s influenced Lisp (e.g., lexical scoping of variables) – It’s still evolving, so it’s a good vehicle for new ideas

8. But I want to learn Lisp! Lisp is used in many practical systems, but Scheme is not Learning Scheme is a good introduction to Lisp We can only give you a brief introduction to either language, and at the core, Scheme and Lisp are the same We’ll point out some differences along the way

9. But I want to learn Clojure! Clojure is a new Lisp dialect that compiles to the Java Virtual Machine Clojure It offers advantages of both Lisp (dynamic typing, functional programming, closures, etc.) and Java (multi-threading, fast execution) We might look at Clojure briefly later

10. DrScheme and MzScheme The PLT Scheme system was developed by a group of academics (Brown, Northeastern, Chicago, Utah)PLT Scheme It’s most used for teaching introductory CS courses MzScheme is the basic Scheme engine and can be called from the command line and assumes a terminal style interface DrScheme is a graphical programming environ- ment for Scheme

11. mzscheme on gl linux1.gl.umbc.edu> pwd /afs/umbc.edu/users/n/i/nicholas/home/courses/331 linux1.gl.umbc.edu> cat test.ss (define (add2 x) (+ x 2)) (define (square x) (* x x)) linux1.gl.umbc.edu> mzscheme Welcome to MzScheme v4.1.1 [3m], Copyright (c) 2004-2008 PLT Scheme Inc. > (load "test.ss") > (add2 3) 5 > (square 1.41421) 1.9999899240999999 > (square (add2 1)) 9 > (exit) linux1.gl.umbc.edu>

12. drscheme

13. Informal Syntax An atom is either an integer or an identifier A list is a left parenthesis, followed by zero or more S-expressions, followed by a right parenthesis An S-expression is an atom or a list Example: () (A (B 3) (C) ( ( ) ) )

14. Hello World (define (helloWorld) ;; prints and returns the message. (printf "Hello World\n"))

15. Square > (define (square n) ;; returns square of a numeric argument (* n n)) > (square 10) 100

16. REPL Lisp and Scheme are interactive and use what is known as the “read, eval, print loop”read, eval, print loop – While true Read one expression from the open input Evaluate the expression Print its returned value (define (repl) (print (eval (read))) (repl))

17. What is evaluation? We evaluate an expression producing a value – Evaluating “2 + sqrt(100)” produces 12 Scheme has a set of rules specifying how to evaluate an s-expression We will get to these very soon – There are only a few rules – Creating an interpreter for scheme means writing a program to read scheme expressions, apply the evaluation rules, and print the result

18. Built-in Scheme Datatypes Basic Datatypes Booleans Numbers Strings Procedures Symbols Pairs and Lists The Rest Bytes & Byte Strings Keywords Characters Vectors Hash Tables Boxes Void and Undefined

19. Lisp: T and NIL NIL is the name of the empty list, ( ) As a boolean, NIL means “false” T is usually used to mean “true,” but… …anything that isn’t NIL is “true” NIL is both an atom and a list – it’s defined this way, so just accept it

20. Scheme: #t, #f, and ‘() Scheme’s boolean datatype includes #t and #f #t is a special symbol that represents true #f represents false In practice, anything that’s not #f is true Booleans evaluate to themselves Scheme represents empty lists as the literal ( ) which is also the value of the symbol null

21. Numbers Numbers evaluate to themselves Scheme has a rich collection of number types including the following – Integers (42) – Floats (3.14) – Rationals: (/ 1 3) => 1/3 – Complex numbers: (* 2+2i -2-2i) => 0-8i – Infinite precision integers: (expt 99 99) => 369…99 (contains 198 digits!) – And more…

22. Strings Strings are fixed length arrays of characters – "foo" – "foo bar\n" – "foo \"bar\"” Strings are immutable Strings evaluate to themselves

23. Predicates A predicate (in any computer language) is a function that returns a boolean value In Lisp and Scheme predicates return either #f or often something else that might be useful as a true value – The member function returns true iff its first argument is in the list that is its second argument – (member 3 (list 1 2 3 4 5 6)) => (3 4 5 6))

24. Function calls and data A function call is written as a list – the first element is the name of the function – remaining elements are the arguments Example: (F A B) – calls function F with arguments A and B Data is written as atoms or lists Example: (F A B) is a list of three elements – Do you see a problem here?

25. Simple evaluation rules Numbers evaluate to themselves #t and #f evaluate to themselves Any other atoms (e.g., foo) represents variables and evaluate to their values A list of n elements represents a function call – e.g., (add1 a) – Evaluate each of the n elements (e.g., add1->a procedure, a->100) – Apply function to arguments and return value

26. Example (define a 100) > a 100 > add1 # > (add1 (add1 a)) 102 > (if (> a 0) (+ a 1)(- a 1)) 103 define is a special form that doesn’t follow the regular evaluation rules Scheme only has a few of these Define doesn’t evaluate its first argument if is another special form What do you think is special about if?

27. Quoting Is (F A B) a call to F, or is it just data? All literal data must be quoted (atoms, too) (QUOTE (F A B)) is the list (F A B) – QUOTE is not a function, but a special form – Arguments to a special form aren’t evaluated or are evaluated in some special manner '(F A B) is another way to quote data – There is just one single quote at the beginning – It quotes one S-expression

28. Symbols Symbols are atomic names > ’foo foo > (symbol? ‘foo) #t Symbols are used as names of variables and procedures – (define foo 100) – (define (fact x) (if (= x 1) 1 (* x (fact (- x 1)))))

29. Basic Functions car returns the head of a list car (car ‘(1 2 3)) => 1 (first ‘(1 2 3)) => 1 ;; for people who don’t like car cdr returns the tail of a list cdr (cdr ‘(1 2 3)) => (2 3) (rest ‘(1 2 3)) => (2 3) ;; for people who don’t like cdr cons constructs a new list beginning with its first arg and continuing with its second cons (cons 1 ‘(2 3)) => (1 2 3)

30. More Basic Functions eq? compares two atoms for equality (eq ‘foo ‘foo) => #t (eq ‘foo ‘bar) => #f Note: eq? is just a pointer test, like Java’s ‘=‘ equal? tests two list structures (equal? ‘(a b c) ‘(a b c)) =#t (equal? ‘(a b) ‘((a b))) => #f Note: equal? compares two complex objects, like a Java object’s equal method

31. Other useful Functions (null? S) tests if S is the empty list – (null? ‘(1 2 3) => #f – (null? ‘()) => #t (list? S) tests if S is a list – (list? ‘(1 2 3)) =>#t – (list? ‘3) => #f

32. More useful Functions list makes a list of its arguments – (list 'A '(B C) 'D) => (A (B C) D) – (list (cdr '(A B)) 'C) => ((B) C) Note that the parenthesized prefix notation makes it easy to define functions that take a varying number or arguments. – (list ‘A) => (A) – (list) => ( ) Lisp dialects use this flexibility a lot

33. More useful Functions append concatenates two lists – (append ‘(1 2) ‘(3 4)) => (1 2 3 4) – (append '(A B) '((X) Y)) => (A B (X) Y) – (append ‘( ) ‘(1 2 3)) => (1 2 3) append takes any number of arguments – (append ‘(1) ‘(2 3) ‘(4 5 6)) => (1 2 3 4 5 6) – (append ‘(1 2)) => (1 2) – (append) => null – (append null null null) => null

34. If then else In addition to cond, Lisp and Scheme have an if special form that does much the same thing (if ) – (if ( foo – (if ( bar In Lisp, the then clause is optional and defaults to null, but in Scheme it’s required

35. Cond cond (short for conditional) is a special form that implements the if... then... elseif... then... elseif... then... control structure (COND (condition1 result1 ) (condition2 result2 )... (#t resultN ) )

36. Cond Example (cond ((not (number? x)) 0) ((< x 0) 0) ((< x 10) x) (#t 10) ) (if (not (number? x)) 0 (if (<x 0) 0 (if (< x 10) x 10)))

37. Defining Functions (DEFINE (function_name parameter_list) function_body ) Examples: ;; Square a number (define (square n) (* n n)) ;; absolute difference between two numbers. (define (diff x y) (if (> x y) (- x y) (- y x)))

38. Example: member member is a built-in function, but here’s how we’d define it (define (member x lst) ;; x is a top-level member of a list if it is the first ;; element or if it is a member of the rest of the list (cond ((null lst) #f) ((equal x (car lst)) list) (#t (member x (cdr lst)))))

39. Example: member We can also define member using if: (define (member x lst) (if (null> lst) null (if (equal x (car lst)) lst (member x (cdr lst))))) We could also define it using boolean ops not, and & or, all built-in (define (member x lst) (and (not (null lst)) (or (equal x (car lst)) (member x (cdr lst)))))

40. Example: define append (append ‘(1 2 3) ‘(a b)) => (1 2 3 a b) Here are two versions, using if and cond: (define (append l1 l2) (if (null l1) l2 (cons (car l1) (append (cdr l1) l2))))) (define (append l1 l2) (cond ((null l1) l2) (#t (cons (car l1) (append (cdr l1) l2)))))

41. Example: SETS Implement sets and set operations: union, intersection, differenceImplement sets and set operations: union, intersection, difference Represent a set as a list and implement the operations to enforce uniqueness of membershipRepresent a set as a list and implement the operations to enforce uniqueness of membership Here is set-addHere is set-add (define (set-add thing set) ;; returns a set formed by adding THING to set SET (if (member thing set) set (cons thing set)))

42. Example: SETS Union is only slightly more complicatedUnion is only slightly more complicated (define (set-union S1 S2) ;; returns the union of sets S1 and S2 (if (null? S1) S2 (add-set (car S1) (set-union (cdr S1) S2)))

43. Example: SETS Intersection is also simple (define (set-intersection S1 S2) ;; returns the intersection of sets S1 and S2 (cond ((null s1) nil) ((member (car s1) s2) (set-intersection (cdr s1) s2)) (#t (cons (car s1) (set-intersection (cdr s1) s2)))))

44. Reverse Reverse is another common operation on Lists It reverses the “top-level” elements of a list – That is, it constructs a new list equal to its argument with the top level elements in reverse order. (reverse ‘(a b (c d) e)) => (e (c d) b a) (define (reverse L) (if (null? L) null (append (reverse (cdr L)) (list (car L))))

45. Reverse is Naïve The previous version is often called naïve reverse because it’s so inefficient What’s wrong with it? two problems – The kind of recursion it does grows the stack when it does not need to – It ends up making lots of needless copies of parts of the list

46. Tail Recursive Reverse The way to fix the first problem is to employ tail recursion The way to fix the second problem is to avoid append. So, here is a better reverse: (define (reverse2 L) (reverse-sub L null)) (define (reverse-sub L answer) (if (null? L) answer (reverse-sub (cdr L) (cons (car L) answer))))

47. Still more useful functions (LENGTH L) returns the length of list L – The “length” is the number of top-level elements in the list (RANDOM N), where N is an integer, returns a random integer >= 0 and < N EQUAL tests if two S-expressions are equal – If you know both arguments are atoms, use EQ instead

48. Programs in files Use any text editor to create your program Save your program on a file with the extension.ss (Load “foo.ss”) loads foo.ss (load “foo.bar”) loads foo.bar Each s-exprssion in the file is read and evaluated.

49. Comments In Lisp, a comment begins with a semicolon ( ; ) and continues to the end of the line Conventions for ;;; and ;; and ; Function document strings: (defun square (x) “(square x) returns x*x” (* x x))

50. Read – eval - print Lisp’s interpreter essentially does: (loop (print (eval (read))) i.e., 1.Read an expression 2.Evaluate it 3.Print the resulting value 4.Repeat from 1. Understanding the rules for evaluating an expression is key to understanding lisp. Reading and printing, while a bit complicated, are conceptually simple. Evaluate the Expression Read an Expression Print the result

51. When an error happens Evaluate the Expression Read an Expression Print the result Evaluate the Expression Read an Expression Print the result On an error

52. Eval(S) If S is an atom, then call evalatom(A) If S is a list, then call evallist(S)

53. EvalAtom(S) Numbers eval to themselves T evals to T NIL evals to NIL Atomic symbol are treated as variables, so look up the current value of symbol

54. EvalList(S) Assume S is (S1 S2 …Sn) – If S1 is an atom representing a special form (e.g., quote, defun) handle it as a special case – If S1 is an atom naming a regular function Evaluate the arguments S2 S3.. Sn Apply the function named by S1 to the resulting values – If S1 is a list … more on this later …

55. Variables Atoms, in the right context, as assumed to be variables. The traditional way to assign a value to an atom is with the SET function (a special form) More on this later [9]> (set! 'a 100) 100 [10]> a 100 [11]> (set 'a (+ a a)) 200 [12]> a 200 [13]> b *** - EVAL: variable B has no value 1. Break [14]> ^D [15]> (set 'b a) 200 [16]> b 200 [17]> (set 'a 0) 0 [18]> a 0 [19]> b 200 [20]>

56. Input (read) reads and returns one s-expression from the current open input stream. [1]> (read) foo FOO [2]> (read) (a b (1 2)) (A B (1 2)) [3]> (read) 3.1415 [4]> (read) -3.000 -3.0

57. Output [1]> (print '(foo bar)) (FOO BAR) [2]> (setq *print-length* 3 ) 3 [3]> (print '(1 2 3 4 5 6 7 8)) (1 2 3...) [4]> (format t "The sum of one and one is ~s.~%" (+ 1 1)) The sum of one and one is 2. NIL

58. Let (let … ) – = ( … ) – = or ( ) or ( ) Creates environment with local variables v1..vn, initializes them in parallel and evaluates the. Example: >(let (x (y)(z (+ 1 2))) (print (list x y z))) (NIL NIL 3)

59. Iteration - DO (do ((x 1 (1+ x)) (y 100 (1- y))) ((> x y)(+ x y)) (princ “Doing “) (princ (list x y)) (terpri))